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    From: Edmund Chao, Rochester, MN

    To: BIOMCH-L Mail Readers,
    Fabio Catani and Herman Woltring

    Date: November 12, 1990

    Subject: Issues related to joint moment calculation

    Dear BIOMCH-L Mail Readers:

    Tom Cahalan has shown me the letters sent by Fabio Catani and the response
    letter by Herman Woltring and I read them with great interest. As a
    noncomputer user, I seem to have missed many of the interesting communications
    through the computer BITNET system and, luckily, I have Tom Cahalan to keep me
    posted on some of the subjects that I have always had an interest in.

    I am deeply sympathetic towards Dr. Catani's problems, and I wish to address
    the issue of joint moment calculation in general and acknowledge that the
    suggested solution and calculation guidelines provided by Herman are the right
    way to go. First of all, we should all realize that the so-called "joint
    moments" currently used in the field are calculated mainly from the externally
    measured forces and the inertial effect of the musculoskeletal system. Hence,
    these are the quantities to be supposedly more reliable without the concerns of
    the Inverse Dynamic Problem and the Redundancy in muscle and joint constraint
    force determination. In order to calculate such moment, accurate determination
    of joint center (2-D) or joint axis (3-D) of rotation is extremely important,
    as stated by both Catani and Woltring. Unfortunately, the limited papers I
    have read in the literature about joint moment analysis have not gone into
    details concerning how these moments were calculated. In fact, when this
    subject was presented at some society meetings, I occasionally asked questions
    related to this concern. On this issue, I wish to raise the following
    fundamental questions.

    1. The calculation of joint moment has many sources of error in addition to
    the relative motion of the markers due to soft tissue movement. The more
    critical issue here is that all the potential measurement errors, including
    ground reaction force magnitudes, the location of such forces and their
    directions, plus the determination of the center of mass as well as the
    inertial properties of the limb segments are all additive in accumulating
    the potential error of such calculation. These do not include the problem
    of locating joint axis of rotation yet. I realize that one may only con-
    cern relative changes instead of the absolute value. But, if the calcula-
    tion will be subjected to so many sources of error, one should question
    the accuracy and reliability of such quantities (i.e., joint moments in
    different planes).

    2. In all seemingly exciting clinical applications, one should provide an
    error bound of all the moment data based on the experimental method and the
    theoretical calculation utilized. Otherwise, only relying on statistical
    analysis, the results and concluding remarks can be grossly misleading. The
    concerns on data normalization with respect to walking velocity or cadence,
    on the temporal occurrence of critical joint moment of concern and on the
    consideration of the entire pattern of moment as a function of time rather
    than looking at discrete instances must be addressed critically. We are
    all waiting to have the most exciting and reliable technique for clinical
    application of gait analysis, but we must also be extremely careful not to
    fall flat on what we have tried for so long to reach such goal.

    3. Finally, the determination of instantaneous axis of rotation in 3-D rigid
    body kinematics or the hypothetical 3-D instantaneous center of rotation
    should be utilized to calculate joint moments. The joint articulating
    surface contact point (even if one could determine it reliably) does not
    necessarily represent the center of rotation, since the type of articula-
    ting surface motion can vary from sliding to spinning type of motion rather
    than rolling without slipping.

    Therefore, I wish to propose that the biomechanicians in the field who are
    interested in rigid body kinematics and kinetcs be more critical of the
    currently reported joint moment papers. There is no doubt in my mind that the
    present instrumentation and technology are able to determine approximately the
    instantaneous helical axes and refer them back to each connecting skeletal
    segment for the purpose of calculating joint resultant moment resulting from
    externally applied forces and the inertial effects. The method outlined by
    Herman appears to be very elegant and practical. The concept of three-
    dimensional instantaneous center of rotation proposed by me about ten years
    ago was only meant to represent a spatial trajectory illustrating the path of
    instantaneous helical axis movement of two loosely connected rigid bodies.
    Strictly speaking, such concept has rather limited utilization, and for the
    purpose of calculating instantaneous joint moment, one must utilize the
    instantaneous helical axis concept described by Herman. Please keep up with
    your excellent work, Herman!

    For those who may be interested in knowing the potential application of joint
    moment to clinical orthopedics, the following excellent references are highly

    1. Podromos, et al., JBJS, 67-A:1188, 1985
    2. Wang, et al., JBJS, 72-A:905, 1990
    3. Berchuck, et al., JBJS, 72-A:71, 1990

    In addition, Kadaba has performed an excellent experiment dealing with the
    issue of repeatability of gait kinematic, kinetic, and EMG data in normal
    adults (see J. of Orthopaedic Research, 7:849, 1989). In Kadaba's article,
    the repeatability issue has been addressed, but unfortunately, the issues of
    accuracy and reliability were not questioned. Such issues should be carefully
    considered, especially when one wishes to calculate the joint moments in the
    frontal plane and for more distal joints (such as the ankle and knee) because
    of the potential error magnification and the inherent technical limitation of
    the motion analysis system due to visual field resolution.

    Sorry I don't have Cappozzo's paper discussing joint moment determination as
    presented in the Bristol ESB meeting, 1987. I would very much like to read
    that to see if Cappozzo's opinion would in any way coincide with my concerns.
    We are dealing with a rather important subject, because our orthopedic clinical
    colleagues tend to take the surface value of a biomechanical article, and we
    must ensure that the data presented do indeed reflect the actual physiological
    phenomena quantitated as accurately as current instrumentation allows. If the
    method used to determine the joint moment is not theoretically correct or is
    technically inaccurate, one must be extremely carefull before making strong
    prognostic or therapeutic statements. I hope that this discussion and my
    personal opinion will stimulate a lot of debate as well as clarification. If
    joint moment can be well established for clinical application, everyone in the
    field should utilize it to its maximum extent. I will be eternally happy to
    see theoretical/objective gait analysis make a giant step forward in its
    practical utilization in orthopedics.


    Edmund Chao
    Rochester, MN

    P.S. Dr. Chao may be contacted through Tom Cahalan